Is the word legumes the same in Brazilian and European Portuguese?

No

While the spelling and grammar are identical, there is a difference in typical usage and semantic scope. In Brazil, "legumes" refers specifically to non-leafy vegetables (such as carrots, potatoes, and zucchini), while "verduras" is the term used for leafy greens (such as lettuce, kale, and spinach). In Portugal, "legumes" is a general, all-encompassing term used for all vegetables, including leafy ones.

Brazilian Portuguese Examples

1. Eu gosto de comer legumes e verduras no jantar. (I like to eat vegetables and leafy greens for dinner.)
2. Comprei legumes e verduras na feira. (I bought vegetables and leafy greens at the market.)
3. A criança não quer comer legumes nem verduras. (The child doesn't want to eat vegetables or leafy greens.)
4. O prato tem legumes e verduras cozidas. (The dish has cooked vegetables and leafy greens.)
5. Preciso de legumes e verduras para a salada. (I need vegetables and leafy greens for the salad.)

Portuguese (Portugal) Examples

1. Eu gosto de comer legumes ao jantar. (I like to eat vegetables for dinner.)
2. Comprei legumes no mercado. (I bought vegetables at the market.)
3. A criança não quer comer legumes. (The child doesn't want to eat vegetables.)
4. O prato tem legumes cozidos. (The dish has cooked vegetables.)
5. Preciso de legumes para a salada. (I need vegetables for the salad.)